Ben Kovitz, who ran the old "Lenore Thomson wiki" (and is very influenced by her as I am) was discussing the functions on a list, and made this great explanation of Ni and its difference from Ne:
"Intuition is guessing—or rather, orienting by what seems to you to be a good guess even though the facts aren't in. Why does it seem like such a good guess? Well, with Extraverted Intuition, you can point out the things [i.e. in the environment="e"] that suggest your guess so that other people start to see the possibility, too; with Introverted Intuition, you can't. WIth Extraverted Intuition, the guess keeps changing as new information is revealed [again, from the environment]: as parts of the big picture get filled in, your guess about the whole absorbs them and revises in unpredictable ways. You need a constant influx of new information to keep triggering you to revise your guesses. With Introverted Intuition, the guess might start "reply hazy, try later" and gradually clarify, but it's somewhat impervious to new information. You search within [individually="i"], ideas come, and you trust them. If information comes in that contradicts the guess, you just tune it out or call it an illusion.
So the Introverted Intuitive attitude aims at getting ahead of all consciously accessible information—including, especially, direct experience."
This seems to be the best explanation I've seen, especially regarding what really makes it "internal" or introverted. (It's often simply called "the unconscious", which he had also just used, but as I pointed out, "unconscious" has several uses, and so Jung and others' definitions with that term never "clicked" for me. I then figured it involved some sort of "impressions" that come up, like "hunches", and I didn't know whether these were just things that were "there" involuntarily, or not, but saying it's a "guess" that you deliberately look within to see what ideas come up, really clarifies it for me). It's the "trust" in these ideas that makes it an introverted attitude. With me, I keep looking on the outside (and this is actually stuff "stored in memory" as Lenore puts it, and this helps me, as "memory" is technically "inside", so it begged the question of the real difference with Ni's "internal" source and Ne's "memory". Ne is memory of externally based patterns (such as "contexts") you can guess from, while Ni is just stuff from the unconscious that you basically seek to fill in the information. (Hence, "freeing sense impressions from their larger [external] contexts" as Lenore puts it).
Me; I'll get these internal images or sense of things, but I don't trust them. They're just "there", and I almost always assume it's "illusion" or irrelevent. (To the point that I did not even know these were what Ni was based off of, and what could also be used to fill in a situation).